Extension Theorems on Weighted Sobolev Spaces and Some Applications

Chua, Seng-Kee

Canadian journal of mathematics, Tome 58 (2006) no. 3, pp. 492-528

Résumé

We extend the extension theorems to weighted Sobolev spaces $L_{w,k}^{p}\left( \mathcal{D} \right)$ on $(\varepsilon ,\delta )$ domains with doubling weight $w$ that satisfies a Poincaré inequality and such that ${{w}^{-1/p}}$ is locally ${{L}^{{{p}'}}}$ . We also make use of the main theorem to improve weighted Sobolev interpolation inequalities.

Détail

DOI : 10.4153/CJM-2006-021-0

Mots-clés : 46E35, Poincaré inequalities, Ap weights, doubling weights, (ε, δ) and (ε,∞) domains

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